The limitation is actually that a particular JI scale cannot be moved to a different key without changing the scale into something else.A purely consonant JI guitar. I get that it's in just one key, but it would be super cool to compose on, as you wouldn't have to worry about the different keys.
However, placing the tonic on different frets results in the modes of the initial JI scale, these are essentially different JI scales, some more dissonant than others.
So (assuming 12 frets per octave) you would have 12 different JI scales to work with, but each fixed to a particular tonic note.